Morse foliations of codimension one on the sphere S^3

Morse foliations of codimension one on the sphere S^3 are studied and the existence of special components for these foliations is derived. As a corollary the instability of Morse foliations can be proven in almost all cases.Comment: 31 pages, 12 figure

Coxeter Polynomials of Salem trees

We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove a relation about multiplicities of eigenvalues of Coxeter transformations of joins of trees.Comment: 9 page

Predicting the Next Maxima Incidents of the Seasonally Forced SEIR Epidemic Model

This paper aims at predicting the next maxima values of the state variables of the seasonal SEIR epidemic model and their in-between time intervals. Lorenz's method of analogues is applied on the attractor formed by the maxima of the corresponding state variables. It is found that both quantities are characterized by a high degree of predictability in the case of the chaotic regime of the parameter space.Comment: 6 pages, 3 figures, 2 tables, typos adde

A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem

Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes the average degree over all subgraphs is solvable in polynomial time but for many networks fails to find subgraphs which are near-cliques. On the other hand, formulations that are geared towards finding near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem. In this work, we propose a formulation which combines the best of both worlds: it is solvable in polynomial time and finds near-cliques when the DSP fails. Surprisingly, our formulation is a simple variation of the DSP. Specifically, we define the triangle densest subgraph problem (TDSP): given $G(V,E)$, find a subset of vertices $S^*$ such that $\tau(S^*)=\max_{S \subseteq V} \frac{t(S)}{|S|}$, where $t(S)$ is the number of triangles induced by the set $S$. We provide various exact and approximation algorithms which the solve the TDSP efficiently. Furthermore, we show how our algorithms adapt to the more general problem of maximizing the $k$-clique average density. Finally, we provide empirical evidence that the TDSP should be used whenever the output of the DSP fails to output a near-clique.Comment: 42 page

Managing the hotel managers: HRM practices in Greek luxury hotels

This paper explores the current HRM practices employed in the international hospitality industry. More specifically it investigates four key HRM areas regarding the work of General Managers (GMs) in luxury (4 and 5*) hotels in Greece namely: recruitment and selection; training and development (focused in managerial competencies); performance evaluation; networking and communication. The dynamic and complex nature of the management function in global hospitality business today and the realisation that what works effectively in one country may not be as efficient in another, has led management scholars and practicing managers in continuous efforts to enhance their understanding of this context and its effects on international (hotel) managers. This paper focuses in the Greek context since the country is among the most popular tourist destinations in the world. The author argues that managerial work and HRM practices in Greek luxury hotels cannot be unaffected from the strong national context, despite the great pressures for standardisation and homogenisation with the international hospitality industry standards. A qualitative research was conducted in 16 luxury (4 & 5*) city and resort hotels in four popular destinations: Athens, Thessaloniki, Crete and Rhodes. In total 32 GMs and their assistants participated in this country case study. The research tool included in-depth semi-structured interviews, the employment of a Personal Competencies Framework (PCF) questionnaire, non participant observations and collection of company documents related to managerial work. All data were triangulated in order to enhance the validity and reliability of this study. The research’s findings indicated that the ‘base requirements’ of managerial work in Greek luxury hotels appear to be similar and compatible with the international industry HRM standards. What actually changes is the level of formality exercised in managerial and HRM practices. A key theme that emerges from this study is the critical role of the hotel’s ownership status. As a concluding point it can be argued that both divergence and convergence contextual forces co-exist and shape the GMs' work in Greek luxury hotels. Further research is needed to fully understand and appreciate the effects of those forces in GMs' work